Angular displacement is usual 2myum fmpxa. 7me*f3)z p)wp;ly express in units of

  Angular velocity is expressed m*-o yzd-z q-g0(prlbin units of

  Angular acceleration is express+t) mr8hhzf*9vyn (bqed in units of

  A boy and a girl are riding on a merry-go-round which ii.k*aw4z,b1u8yt ggy s turning at a constant rate. The boy is near the outer edge.yga yw,zkg ub i4*t18, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a cje* vw f+2qw2gonstant rate. The boy is near thewe2fw +vj*q2g outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at acion8q;3l(z/5 0wxkoit sly , constant rate. The boy is near the outer edge, and the girl is closer to the center. Whnl3iki (soo5x, 8wc/yzl 0t; qo has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a conr2o ea7qlb*,ddve*. q.ql4l mstant rate. Th darq l d*7l4vee2,o. .*lbqmqe boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding nxs6v8ue9q k8 a,y3qla merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is clq k63 ,vl squenya889xoser to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rot nee nt(*) wqyu.ud4)kating. Which of the following is an accurate stateme)enuy t4d.uek() n w*qnt?

  Rolling without slipping de*ifeuudfd+, e2o8kn jsin j 3and14- .pends on

  Two equal forces are applied to a door. The fir:fks e gu.85a ad w(dumoi+,q4st force is applied at the midpoint of the door; the second force is applied at the doo+54dwa.,daku s8: efou mg(i qrknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are as. jrp4yz emq5cco;ig77 g/ b2pplied to a door at the doorknob. The first force is applied perpendicular to the door; the second for7j;bcs 2m7zg 54cqirg/py. e oce is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicurwq,oc /ff1h u)n48vo1h0 bp mu1vd4 dlar to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of u 40fwrd1uvopb 4f1/,v8)dm hqcon h1the second is

  What is the quantity used to measure an object's resistancd;hels01 oti+ e to changes in rotation?l1 o;0di+tsh e

  Consider two uniform solid spher/6e o)euasppxh9/ v; ues where both have the same diameter, but one has twice the mass ofs/u9h; / v6 o)exeppua the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the ramp p;1qs9noaqk ;b*x 9dius of the other. The ratio of the larger sphere's moment of inertia to thap bxnmps* 1a9oqk9;q;t of the smaller sphere is

  Consider two uniform solid spheres where one has twice the masu7wx5.m;g* ry c4dkgcs and twice the diameter of the other. 4x7 kugcd.g;wy*rm5 c The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increaxi1b-gwa u9z+fqn27s sed to 2M and 3R, what ha1+ -2qgw ains 7fbx9uzppens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that obje fpxz8kfc 5*3 * zza:he5yop-kct will

  The moment of inertia of a s o :021au1xa:fc oppsoolid cylinder about its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which hassu 4tfv r9g4h5 a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheeurgtv 54f4s 9hls are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls v8gvo-iegr7e / (z,vrwithout slipping down an inclined plane starting from rest. The linear vo(eevi,-rv8zg7 gvr /elocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of ml41,sy 2im b9fgxn3ab ass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere a g1sbnm, a iy2fl943xbt the bottom of the incline depends on

  "The total angular momentum of a system of particles cha9wd-2g6,f m ,rdkg+zngcrt*dnges when a net external force acts on the system." This state2nc dz, +grdgm6gr ,k9dw-f *tment is

  In what circumstances can the angular velocity of system+hm6 fkcilj(( of particles change without any change in the system's angular moment +6 f(jc(kmhlium?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which maya1jj3wf 2:bw gj r+wbm8rx.l- be present. What happens over time to the Earth's angu+wm:j .83 xb-jajr 1bw wrl2gflar momentum about the Sun?

  The Earth moves about the Sulatwde/43 ;0v00 r*xqiw x;q cwngd8dn in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the 8de00cd;wral/ *wwx 0i3xntg;qq dv4 orbiting speed of the Earth about the Sun?

  An ice skater performs a piroh 4sk+-q9 z.y jy;n v6loml9wouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momen joq9-. +mknol l9vzyh;46wsytum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outnhb 3ura3*w9:x,nld9 pb kt+rstretched arms close to his body. What happens to his rotati3 t nkruw3rpn+xahb:l9d, *b 9onal kinetic energy about the axis of rotation?

  An ice skater performs a pi2-k mj sr-9bej761j4 fmec7 wl1ffu +hu:wdk arouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the ax - rem2 lfk hmw1k:j6wu-s1+ fuf7e74d9jca bjis of rotation?

State the law of conservation of angu+wa h0enz6ybp44rk 2 ular momentum.

  What arc length does the Earth travel i+dgrzdh d f22p(w -gct ,bu4,jn a three month period in its nearly circul zpfj,c(2r u+h dbgdd,-tw24gar orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a l7 shmy7fslf6g qviy1f4/r7e 8 ength of 0.30 m. What distance does the tip of the second hand sweep through in 3 mi /s6eyl4 g17yfvsqrfhif 77m 8nutes and 45 seconds?

  How many rad/s is 25 revolutions per min91 acgq/a rzkf;pv:l8ute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions inisx 4 k;: ghu,m4lz,ct 4.0 s. What is the4i cl zgk 4m:uhs;x,t, frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency off a9c*)i ekr h oq8.8ep:6llod 0.40 kHz. The .i*fkeor elh 986qp oca)ld8:period of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.2d7.pug ymiwj3fv( ckl/-bvvi 6 jj9.00 f6wydl7jp(kv. -mi igv. 3b9 0jcjvu/s?

  A wheel of diameter 26 cm turns at 15- de+yow2h 3ilpz49h uu 3mzr(00 rpm. How far will a point on the outer rim move in3r-3lmzo wey ui4z+29u(phd h 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions ijkh yhtxwn3ca18)+ 7 mn 4.0 s. What is the wy+hh7j1)manxk c8t3 average angular speed of the wheel?

  A bicycle wheel rotates uniformly through:5ihze ,jf j :u+5fa; 3bq0vzk5u:xn4saa w cu 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m fromn::f,j3uwx 4f5 a euzuzhs 05 a+:c ib;5kjavq the center of the wheel?

  A cable car at a ski resort carries skiers a distanzi o(3cy7ni2gce of 6.8 km. The cable which mo o72cni(zy3g ives the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a cor + jiqc-) vr-spdctup1q9r;7nstant angular speed of 2.0 rad/s. Whats7qji+dpcrr-1u 9 q-tr)vp c; is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powe + yuj-fyltym9 3s*c5nred weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of mtc f+5lsn* 9uyy jy-3the cord?

  A wheel of radius 1.0 m is rotating wiim:fw76*mszt+ 6g22q kf sb)kh-jd r kth a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a pos )m: mqb*dk ktf2 62wk jrz+6i-s7fhgint on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a 1 t5 y3atvrj z4khj:ec3mlqr .29xzv0bicycle wheel of diameter 70.0 cm when the b ta3rv5j ez:xzvmtc0 r 4h1 y3kjl29.qike is moving 8.00 m/s?

  How many revolutions per minute (rpm )c5jmsa89x rb) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial grav8xr scj m5a9)bity of $9.80 \; m/s^2$?

  A car is negotiating a flat circmp .lemr). *ksular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (pr*. )rpmskml. eovided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve * nuvz/e. ii*p2 at8xkof radius 50 m with a speed of 20 m/s. The maximum centripetal force z 28e.**ip kux/taivn (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end)c,yz:iy bdnk:4 ex8p of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass have if the string is not p,8byz :ci dkexy)n4: to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rollcf14hp 8l*76hfv g .ysdcspb-s without slipping 10 m down a lane at 4.3 b8 chds46l.v-1 s *f7chpgpf ym/s.
(a) Calculate the angular displacement of the bowling ball.   rad ( fill in numbers only)
(b) Calculate the angular velocity of the bowling ball   rad/s ( fill in numbers only)
(c) Calculate the radial acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)
(d) Calculate the tangential acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)

  A wheel accelerates with a constant angular aj53jhlhqr3sp 6ki r+y h(d(r6;ku lkd9v;+f zcceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angle the wheel rotates through in 2.0 s?

  A wheel accelerates with a constanth/+x6;* pbk vlfg v/rg angular acceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does a 0.300-doil5 uw4/p )dpv7 c9am radius automobile tire rotate after starting from rest and accelerating at a constant d5opw)/pu di79cvla4angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, aiu9kq u5z )kv)nd has an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a constant angt-* a0kx,jhdbh9ha.osj 48ct ular acceleration o .h-j*kbsx49, ahdhc0a8tt j of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while turni eyfox-w)/a0 png through 2.0 revolutions. What isf0 /apoxeyw-) the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm sl1*eeu b5,:zt9moj g2+g qhsoeows down uniformly from 8.40 m/s to rest over a distance of 115 m. What i obzg tj:*q1og e9 h5e,s+2emus the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s t4sd-7b rpmh 6io rest over a distance of 115 m. What is the angulars74 pd 6-ihbrm acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to res dypufp,ok11m 3u56 rct over a distance of 115 m. How long does it take for the wheel to com3p5 pou 1 ckryd,1u6mfe to the stop?

  A centrifuge in a medical laboratory rotates at5ybo 9m9w r2al a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angulrm9ob95 y lwa2ar acceleration before coming to rest.
(a) Determine the initial angular speed of the centrifuge.    $rad/s$
(b) Determine the angle (in radians) through which the centrifuge rotates before coming to rest.    $rad$
(c) Calculate the constant angular acceleration of the centrifuge.    $rad/s^2$
(d) Calculate the time necessary for the centrifuge to come to rest.    $s$

  The bolts on a car whx4 cux; b92()dsq)cklxj( gx neel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required;4nx)jx2 sulc)kx (b dg(xc9q when the force is perpendicular to the wrench?

  The bolts on a car wheel requ41i7xz v3z1g:bs pjvldb6 no )ire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of 7objd43xb vzv:6inz1l p gs1) the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner o5(/c d v68bry2kk+qmo6gtz ntia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mass m is at the origin, mass hln-5h / )mnlt tuq0z3u2f6i q2m is at x = a, and, mass 3m is at x = 2a. - /063nhuil)uq q5 mznh 2ftltWhat is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thoud ,+7qtblik +tqv x.b)ght the center O. A rope wrapped artq++blv , bd t.qikx)7ound the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis t ypm;gzn+s.o0 hought the center O. A rope wrapped around the outer spn g; z.o0+myradius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is iniisd-d5() n ,ax4djrt ktially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceles- dr,d)kj5(x tani d4ration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg.mv5mm x(u74 ol7vm 9cr Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.0 cm for 4.1 s, vvmu5mx74o 7m l(c9mrwhat linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of bs2fe y6g j,qtw:m n96mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of th9:y6fjns2 mtq,we6 bge pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictia x7w+nu3g5kk onless disk pulley of mass 7.07 kg and radius 66.0 cm. kukwan+ 7x53 g What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required ta zt 0 e**kr:q+nirnopn11+brrhm, f*o store $1.00 \times 10^{6} \; J$ of energy when rotating at 400 rad/s, what is the moment of inertial of the wheel in $kgm^{2}$?

  A wheel of moment of iner2nna x q,91jxpp 1,yvetia of $5.00 \; kgm^{2}$ starts from rest and accelerates under a constant torque of 3.00 Nm for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s?

  A solid sphere of mass 1.0 kg and radius 0.010 m )((hlhf vr+z ay/5gfkstarts from rest and rolls without slipping down a 1.0-m high inclined plane. What hrzvk/(+g(y)fl ha5 fis the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 aczx+9wm1 :lj m rolls with a speed of 10 m/s. How high up an inclined plane can aw1mxj:+c 9 zlit climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowei tl0zo *ho,p/f q(zo6d to roll down an inclined plane. How fast is it moving after dropping a vertical dist 6l ifoo(zz*p oq,th0/ance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls 8o+ mz -6rfdyiwithout slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inert -z6i8 or+ydmfia of a sphere is given by $I = (2/5)MR^2$.
(a) Calculate the linear speed of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere at the bottom of the incline.
(c) Does the linear speed depend on the radius or mass of the sphere? Does the angular speed depend on the radius or mass of the sphere?

  An object's angular momentum x7xn/:l) 8k0hos pwvcchanges by $20 \; kgm^{2}/s$ in 4.0 s. What magnitude average torque acted on this object?

  A proton of mass $1.67 \times 10^{-27} \; kg$ rotates with an angular speed of 2 x 106 rad/s in a circle of radius 0.80 m in a cyclotron. What is the orbital angular momentum of the proton?

  An ice skater has a , qo39y6wkicfmoment of inertia of $5.0 \; kgm^{2}$ when her arms are outstretched. At this time she is spinning at 3.0 revolutions per second (rps). If she pulls in her arms and decreases her moment of inertia to $2.0 \; kgm^{2}$, how fast will she be spinning?

  A figure skater rotating at 5.00 rad/yf;n;b8yg(jw z-4i2jdd rkq . s with arms extended has a moment of inerti; 8dyfqyjz 2bnw-r(j.i; kd4ga of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?